# Certified Reduced Basis VMS-Smagorinsky model for natural convection flow in a cavity with variable height

## TL;DR

This paper introduces a certified reduced basis model for natural convection in a variable height cavity, incorporating physical and geometric parameters, and demonstrates its effectiveness through numerical tests.

## Contribution

The work develops a novel reduced basis VMS-Smagorinsky model with an empirical interpolation and error estimation for parametrized natural convection problems.

## Key findings

- Effective reduced basis model for variable height cavities
- Accurate approximation of sub-grid eddy viscosity terms
- Successful numerical validation across parameter configurations

## Abstract

In this work we present a Reduced Basis VMS-Smagorinsky Boussinesq model, applied to natural convection problems in a variable height cavity, in which the buoyancy forces are involved. We take into account in this problem both physical and geometrical parametrizations, considering the Rayleigh number as a parameter, so as the height of the cavity. We perform an Empirical Interpolation Method to approximate the sub-grid eddy viscosity term that let us obtain an affine decomposition with respect to the parameters. We construct an a posterior error estimator, based upon the Brezzi-Rappaz-Raviart theory, used in the greedy algorithm for the selection of the basis functions. Finally we present several numerical tests for different parameter configuration.